Calculating the Bending Modulus for Multicomponent Lipid Membranes in Different Thermodynamic Phases

Abstract

We establish a computational approach to extract the bending modulus, KC, for lipid membranes from relatively small-scale molecular simulations. Fluctuations in the splay of individual pairs of lipids faithfully inform on KC in multicomponent membranes over a large range of rigidities in different thermodynamic phases. Predictions are validated by experiments even where the standard spectral analysis-based methods fail. The local nature of this method potentially allows its extension to calculations of KC in protein-laden membranes.

Lipid Domain Co-localization Induced by Membrane Undulations

“…A case in point is the development of membrane undulations at finite temperature, which in turn gives rise to algebraically decaying, fluctuation-induced interactions between membrane inclusions that are more rigid or softer than the background phase (15)(16)(17)(18)(19). Importantly for the present problem, it is well-known that the Lo domains are more rigid than the Ld ones, with a bending rigidity of k Lo $ 2 À 3 k Ld (20,21). Thus, these lipid domains should experience an entropic interaction mediated by membrane undulations.…”

“…11, and solve for dk to yield a relatively modest bending rigidity heterogeneity, dkz50:25 k 0 . In light of the fact that k Lo $ 2 À 3 k Ld in synthetic membranes (20,21), membrane undulations alone are thus sufficient to co-localize Lo/Ld domains in model membranes. We note that applying Eq.…”

“…Non-perturbative analysis of membrane undulation effects on L fluct : special case Although the above analysis captures the effect of membrane undulations on interleaflet coupling for small elastic heterogeneity ðdk ( k 0 Þ, drawing quantitative conclusions for Ld/Lo systems (for which elastic heterogeneity can be as large as dkz2k 0 (20,21)) from a simple perturbative approach becomes questionable. To complement the results of the perturbative analysis leading to Eqs.…”

Cholesterol under oxidative stress—How lipid membranes sense oxidation as cholesterol is being replaced by oxysterols

“…To quantify the free energy cost of sterol tilting in a lipid membrane, we used a previously established protocol to extract the tilt modulus, χ, from the sterol tilt (θ; θ¼0 describes the sterol tilt where its ring plane is parallel to the bilayer normal) probability distributions P(θ) that are obtained from atomistic MD simulations [80,81]. A quadratic fit was performed to an expression of the form À k B T ln ½PðθÞ= sin θ over an angular interval chosen to represent the best-sampled angular region and at the same time to limit the fit to the low θ regime, where the quadratic expansion of the free energy with respect to tilt is valid.…”

“…Finally, χ was determined from the coefficient that corresponded to this fit (additional details of this methodology can be found in Refs. [80,81].…”